A large number of independent schools have pledged to open their doors to talented pupils from non-privileged backgrounds if the Government agrees to pay part of their fees.

The high-performing institutions said they wanted to admit bright children regardless of family income, arguing the move would be the "single biggest policy step" towards boosting social mobility.

A total of 80 independent day schools are in support of a state-funded Open Access scheme that would see them match fee subsidies from the Government with money from their own bursary funds.

The programme, in which parents pay a sliding scale of fees according to their means, has been piloted at the Belvedere School in Liverpool over a seven-year period.

Headmasters from 44 independent schools have thrown their weight behind the scheme in a letter to The Times.

The signatories said: "As heads of some of the most successful independent day schools in the country, we would like to admit pupils on merit alone, irrespective of whether their families can afford fees.

"We have a proud history of educating a wide social mix and we are determined to extend that opportunity.

"Supporting Open Access is the single biggest policy step the Government could take to boost social mobility at the top of society and bridge the divide between the state and independent sectors."

The heads, including those of City of London School, Dulwich College and the Grammar School at Leeds, said the pilot showed that entry on merit to independent day schools costs less than a state school place.

Sir Peter Lampl, the chairman of the Sutton Trust which has championed the idea, claims more than 30,000 bright children who cannot currently afford to go to independent school would be able to if Open Access was introduced.